Question

How many different ways can four team members from the group of fifteen be lined up for a photograph?

Answer 1

Answer:

32760

Step-by-step explanation:

This is a permutation of 15 objects taken 4 at a time.  To calculate this, we use the formula:

$_nP_r=\frac{n!}{(n-r)!}$

In our case, n is 15 and r is 4:

$_{15}P_4=\frac{15!}{(15-4)!}=\frac{15!}{11!}=32760$

Answer 2

The different ways of four team members from the group of fifteen be lined up for a photograph are $\boxed{32760}.$

Further explanation:

The formula of permutation can be expressed as,

$\boxed{^n{P_r}= \frac{{n!}}{{\left({n - r} \right)!}}}$

Here, “n” represents the total observations and “r” represents number of the observation has to be arranged.

Given:

Total number of members in group is 15.

Four members from a group of 15 are lined up for a photograph.

Calculation:

The total number of different ways of four team members from the group of fifteen be lined up for a photograph can be calculated as follows.

$^n{P_r}=\dfrac{{n!}}{{\left({n - r} \right)!}}$

Substitute 15 for n and 4 for r in above equation

$\begin{aligned}^{15}{P_4}&= \frac{{15!}}{{\left( {15 - 4}\right)!}}\\&=\frac{{15!}}{{11!}}\\ &=\frac{{15 \times 14 \times 13 \times 12 \times 11!}}{{11!}}\\&= 15 \times 14 \times 13 \times12\\&= 32760\\\end{aligned}$

Hence, the different ways of four team members from the group of fifteen be lined up for a photograph are $\boxed{32760}.$

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445

2. Learn more about range and domain of the function brainly.com/question/3412497

3. Learn more about profit and loss brainly.com/question/2479097

Answer details:

Grade: High School

Subject: Mathematics

Chapter:Permutation and Combination

Keywords: different ways, select, combination, randomly picks, permutation, photograph, team members, group of fifteen, lined up, permutation.